Cambridge International Mathematics

EXERCISE 22C

1 Revisit theOpening Problemon page 455.

a Calculate the equation of the line of best fit using linear regression.

b Use the equation of the line to predict the weight of a 200 cm tall football player.

2 Tomatoes are sprayed with a pesticide-fertiliser mix. The figures below give the yield of tomatoes per

bush for various spray concentrations.

Spray concentration,xml per 2 litres 2 4 6 8 10 12

Yield of tomatoes per bush,y 45 76 93 105 119 124

a What is the independent variable?

b Draw a scatter diagram for the data.

c Calculate the equation of the linear regression line using

technology.

d Interpret the gradient and vertical intercept of this line.

e Use the equation of the linear regression line to predict

the yield if the spray concentration was 7 ml.

Comment on whether this prediction is reasonable.

3 The data below show the number of surviving lawn beetles in a square metre of lawn two days after it

was sprayed with a new chemical.

Amount of chemical, xg 2 3 5 6 9

Number of lawn beetles, y 11 6 6 4 3

a What is the dependent variable? b Draw a scatter diagram for the data.

c Use technology to determine the equation of the linear regression line.

d Interpret the gradient and vertical intercept of this line.

e Use the regression line to predict the number of beetles surviving if 7 g of spray

were used. Comment on whether this prediction is reasonable.

4 The yield of cherries depends on the number of frosty mornings experienced by the tree. The following

table shows the yield of cherries from an orchard over several years with different numbers of frosty

mornings.

Frosty mornings (n) 18 29 23 38 35 27

Yield (Y) 29 : 4 34 : 6 32 : 1 36 : 9 36 : 1 32 : 5

a Produce a scatter diagram ofYagainstn.

b Find the linear model which best fits the data.

c Estimate the yield from the orchard if the number of frosty mornings is:

i 31 ii 42 :

d Complete: “The greater the number of frosty mornings, the ....... the yield of cherries.”

5 Carbon dioxide (CO 2 ) is a chemical linked to acid rain and global warming. The concentration of CO 2

in the atmosphere has been recorded over a 40 year period. It is measured in parts per million or ppm

found in Law Dome Ice Cores in Antarctica.

Year 1960 1970 1980 1990 2000

CO 2 concentration (ppm) 313 321 329 337 345

Two variable analysis (Chapter 22) 465

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